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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
5
votes
1
answer
212
views
Is there a name for this variant of the category of elements of a profunctor?
Let $\mathsf{C}$ be a category and let $P : \mathsf{C}^{\text{op}} \times \mathsf{C} \to \mathsf{Set}$ be a functor.
Let $\mathsf{E}$ be the category whose:
objects are pairs $(X,x)$, where $X$ is an …
16
votes
Are functor categories with triangulated codomains themselves triangulated?
I believe I have a simpler counterexample, which I learned from Paul Balmer's course on tensor-triangular geometry last spring:
Claim The arrow category $\mathcal{T}^{\bullet \to \bullet}$ of a triang …